Related papers: A shift-optimized Hill-type estimator

Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…

Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…

Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…

We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…

Taylor's Law (TL) relates the variance to the mean of a random variable via power law. In ecology it applies to populationsand it is a common empirical pattern shared among different ecosystems. Measurements give power law exponent to be…

``When a measure becomes a target, it ceases to be a good measure'', this adage is known as {\it Goodhart's law}. In this paper, we investigate formally this law and prove that it critically depends on the tail distribution of the…

Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing…

The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if $\hat{\alpha}_n$ is an…

This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…

We use the so-called t-Hill tail index estimator proposed by Fabi\'an(2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of loss. Under the second-order condition of regular variation, we establish…

This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model.

Based on the methods provided in Caeiro and Gomes (2002) and Fraga Alves (2001), a new class of location invariant Hill-type estimators is derived in this paper. Its asymptotic distributional representation and asymptotic normality are…

Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…

Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric,…

Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a…

In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…

We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a…

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal…